Three-Axis Magnetometer Calibration based on Optimal Ellipsoidal Fitting under Constraint Condition for Pedestrian Positioning System Using Foot-mounted Inertial Sensor/Magnetometer

Indoor pedestrian positioning is a technology for indoor pedestrian to provide position information. Global Positioning System (GPS) is the most widely used positioning system in the world at present, the accuracy of GPS in the indoor environment cannot meet the requirements because the GPS signal is extremely attenuated by the architectural shelter. Hence, the indoor positioning system without GPS has become a hot spot for research. The inertial sensor is an autonomous navigation and positioning sensor, which does not rely on external information, the position information of indoor pedestrian can be obtained by calculating the data collected from inertial sensor (accelerometer and gyroscope). It is an effective method to illustrate inertial device on the foot of pedestrian, which is called a pedestrian positioning system based on foot-mounted inertial sensors. Due to the accumulative error increased with time, the positioning system based on inertial sensors cannot provide accurate position information alone during a long time. Hence, the Zero Update (ZUPT) algorithm is proposed to effectively limit the accumulative error of inertial sensor. However, the heading error is unobservable when the velocity is used as the observation, which further limits the positioning accuracy of the indoor pedestrian positioning system based on foot-mounted inertial sensor. The heading information calculated by the output from magnetometer can be an effective observation to assist the foot-mounted inertial sensor. However, magnetometer is susceptible to environmental interference magnetic field, which can reduce the accuracy of the heading information obtained from magnetometer. Hence, the magnetometer calibration is the key to improve the accuracy of observation and achieve high precision indoor pedestrian positioning based on foot-mounted inertial sensor/magnetometer. Three-axis magnetometer interference can be effective suppressed by optimal ellipsoidal fitting based on least square, the algebraic distance equation between measured value and fitted ellipsoid is establish, all magnetometer error parameters can be obtained by calculating the equation. However, the deviation of the measured value from the theoretical value reduce the rank the calculated matrix, many results are obtained rather than the optimal result. To solve this problem, three-axis magnetometer calibration based on optimal ellipsoidal fitting under constrained conditions is proposed. The magnetic interference model is established at first, which can be described by ellipsoid model, then establish the algebraic distance equation between measured value and fitted ellipsoid, the constraint condition can be obtained by constraining the three-dimensional surface to an ellipsoid. The optimal ellipsoidal fitting under the constraint condition is used to calculate magnetometer parameters and compensate the magnetic interference to improve the accuracy of the heading information obtained from magnetometer. The MTi-G710 (integrated accelerometer, gyroscope, magnetometer, barometer, GPS receiver and Beidou receiver) produced by Xsens company is adopted to complete the actual test, which includes Offline turntable test and indoor pedestrian positioning test based on foot-mounted inertial sensor/magnetometer. The ellipsoid fitting effect based on the proposed magnetometer calibration algorithm is obtained in the offline turntable test. In the indoor pedestrian positioning test based on foot-mounted inertial sensor/magnetometer, the pedestrian movement system model and observation model are established, the result of pedestrian is obtained by the data fusion based on foot-mounted inertial sensor/magnetometer, the correctness and effectiveness of the proposed algorithm are verified.